This model comes with a few problems:
1) High quality games that are meant to be completed quickly will make less money relative to poor quality games that stretch out gameplay.
2) Developers become incentivized to stretch out gameplay to increase revenue.
3) Amazon Underground is covering the costs for now. But if users were asked to pay themselves, I'm sure many would balk at the idea of paying per-minute to play games.
All that aside, this is an interesting idea. I could see episodic games particularly benefiting from this model -- so long as they don't fall into the trap of stretching out gameplay to increase revenue.